Aleandro was the daughter of actor Pedro Aleandro. During the late 1970s, she was vocal about her progressive views and during the rule of the military government she was exiled to Uruguay. Later Aleandro moved to Spain and did not return to Argentina until after the military junta fell in 1982.
Back in Argentina she returned to the stage with Master Class and won the "María Guerrero" award in 1996. The same year she was honored as Ciudadano Ilustre de la Ciudad de Buenos Aires ("Illustrious Citizen of the City of Buenos Aires").
She has so far co-starred five times with fellow actor Héctor Alterio: Los siete Locos (1973), the Academy Award-nominated The Truce (1974), The Official Story (1985), Son of the Bride (2001) and Cleopatra (2003), the last three of which they played husband and wife.